Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
478 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#88544 | C2 | semidirect |
| 2. C9×#938 | C2 | semidirect |
| 3. #11721038 | C2 | semidirect |
| 4. C2×D3×C9⋊C8 | C2 | semidirect |
| 5. C3×#63392 | C2 | semidirect |
| 6. #11720267 | C2 | semidirect |
| 7. #11720263 | C2 | semidirect |
| 35. #63392 | D3 | semidirect |
| 53. C3⋊(C9⋊C8) | D4 | semidirect |
| 96. C2×D3×C9 | D8 | semidirect |
| 103. #938 | D9 | semidirect |
| 242. C3×C9 | #466 | semidirect |
| 341. C2×D3 | #3673 | semidirect |
| 356. C9 | #4775 | semidirect |
| 407. C3 | #10588721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88544 | 2 |
| C9×#938 | 2 |
| #11721038 | 2 |
| C2×D3×C9⋊C8 | 2 |
| C3×#63392 | 2 |
| #11720267 | 2 |
| #11720263 | 2 |
| #10591449 | 3 |
| #10588721 | 3 |